\newproblem{lay:6_2_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.2.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $\mathbf{u}_1=\begin{pmatrix}-1\\4\\3\end{pmatrix}$, $\mathbf{u}_2=\begin{pmatrix}5\\2\\1\end{pmatrix}$, and $\mathbf{u}_3=\begin{pmatrix}3\\-4\\-7\end{pmatrix}$.
	Is the set $S=\{\mathbf{u}_1,\mathbf{u}_2,\mathbf{u}_3\}$ orthogonal?
}{
   % Solution
	To check whether $S$ is orthogonal, we calculate all possible inner products to check if they are 0 or not
	\begin{center}
	  \begin{tabular}{l}
			$\mathbf{u}_1\cdot\mathbf{u}_2=6$\\
			$\mathbf{u}_1\cdot\mathbf{u}_3=-40$\\
			$\mathbf{u}_2\cdot\mathbf{u}_3=0$\\
		\end{tabular}
	\end{center}
	Only $\mathbf{u}_2$ is orthogonal to $\mathbf{u}_3$. The rest of vectors are not orthogonal to each other, and consequently, the set $S$ is not orthogonal.
}
\useproblem{lay:6_2_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
